Yep that is the cap and what that guy did is exactly what I wanted to avoid when I asked about the cap on Terry's forum back in 2012. The same VFD hate happened back on that thread in 2012 too
On our well cap the pump guy screwed a lifting eye in place of the center bolt when he attempted to pull it.
The pump guy said if the casing fails above the pump there could be lots of sediment on top of the pump making it hard to get out. Inspection cameras are $200 to $300 to rent around here, but it is money thrown away if it cant get past the pitless or if the well is silted up above the pump covering the failed section from view. All this money and effort hoping that a steel pipe in the ground 52 years hasn't corroded through anywhere along its length and that it still has at least 15 years of life left seems like a bad gamble imo.
I also find it difficult to understand where the small stones in the water filters are coming from if the casing is still good. I wouldn't think the upward water velocity in the 4" casing from pumping 10 gpm would be able to lift small stones from down where the screen might have failed. With a failed screen do sediment and stones gradually build from the bottom up in the casing?
I would distinguish between the casing, aka the pipe between the surface and the water table keeping the soil out and the screen down at the bottom keeping the sand/gravel in the aquifer out of your well casing and pump. If you have sand or gravel in your water, it could come from a failed well casing, or it could come from a failed/failing screen. Since screening is pretty light weight, my bet would be on the screen, but it certainly also could be the well casing. The screening is not that hard to fix. Fixing the casing is more complicated, but not undoable, though it is often cheaper and easier just to drill a new well.
To answer your question about the rocks and gravel, once the screen gets a hole, the flow of water will continue to suck sand and gravel in. It is important to remember that in water, rocks and gravel have a lower apparent density due to the displaced water, making them easier to transport. The ability of water to move sediment goes up with the velocity to the sixth power (more or less), meaning a small hole in a screen will be extremely effective at spraying sand into the well casing. The low pump pressure suggests to me that your pump impellers have eroded, probably from pumping the sand and gravel that you have been finding in your filters.
$40 will get you a 16' inspection camera that would let you check what is under your well cap...
Well drillers can, and should in my opinion, have a great knowledge and experience, but speaking from personal experience, it can really vary. I've had guys who not only didn't understand the importance of galvanic isolation, but also could not tell brass from galvanized in their own gear. (A locker of plumbing fittings drifted a foot deep, not kept clean, and not sorted by size, or material. I had to find them the right pieces out of their pile. Even a couple of buckets would have gone a long way.)
Ever heard the one about the well drilling company that wouldn't buy all wheel drive trucks? They didn't want their crews to get too confident and get stuck. I.e. leaving the landowner to tow the two wheel drive truck into position...
And for what it is worth, I'm a fan of VFDs, but in my experience lots of folks dump on them without understanding them in detail, and certainly not understanding the ins and outs. I don't get it. I feel like it is another "well my brand of truck/tractor/whatever is better than yours, period, no matter what you say or the facts are". Are VFDs as simple as a pressure switch? No, but that is the pro and con. Are there bad ones out there? Of course! But there are reputable brands and vendors, too. I think it is illustrated in the following effect;
(Notice that I have opined a bunch here...)
All the best,
Peter
